Question

Can someone please help me find the value of X?

Answer 1

`x=106\degree`

Step-by-step explanation

We want to find the measure, x.

From the diagram, we see that x represents the central angle (or angle of the arc) for the sides of the triangle.

This means that each of the unknown two angles of the triangle is half the measure of x. This is because the angle formed at the circumference by an arc is half the central angle of the arc.

Therefore, using total angles of a triangle:

`\begin{gathered} 74+(1)/(2)x+(1)/(2)x=180 \\ \Rightarrow74+x=180 \end{gathered}`

Solve for x by collecting like terms:

`\begin{gathered} x=180-74 \\ x=106\degree \end{gathered}`